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arXiv:1506.02512

On the inhomogeneous T-Q relation for quantum integrable models

Yupeng Wang, Wen‐Li Yang, Cao, Junpeng, Kangjie Shi

Published Jun 8, 2015• 1 citation
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Abstract

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial extension of Baxter's T-Q relation [2].
DOI
10.48550/arxiv.1506.02512

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The generic quantum τ 2-model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions of the recursive functional relations in τ j -hierarchy) with generic site-dependent inhomogeneity parameters are given in terms of an inhomogeneous T − Q relation with polynomial Q-functions. The associated Bethe Ansatz equations are obtained. Numerical solutions of the Bethe Ansatz equations for small number of sites indicate that the inhomogeneous T − Q relation does indeed give the complete spectrum.
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